Hazard processes and martingale hazard processes

2008/07/30 by Coculescu, Delia, Nikeghbali, Ashkan
#60G07 #60G44 #60G99 #FOS: Economics and business #FOS: Mathematics #Probability (math.PR) #Risk Management (q-fin.RM)

paper · doi:10.48550/arxiv.0807.4958

Abstract

In this paper, we provide a solution to two problems which have been open in default time modeling in credit risk. We first show that if τ is an arbitrary random (default) time such that its Azéma's supermartingale Z_t^τ=¶(τ>t|\F_t) is continuous, then τ avoids stopping times. We then disprove a conjecture about the equality between the hazard process and the martingale hazard process, which first appeared in \citejenbrutk1, and we show how it should be modified to become a theorem. The pseudo-stopping times, introduced in \citeAshkanYor, appear as the most general class of random times for which these two processes are equal. We also show that these two processes always differ when τ is an honest time.

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